(D) The time period of a pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$.Taking the derivative,the change in time period is $\frac{dT}{T} = \frac{1

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(D) The time period of a pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$.Taking the derivative,the change in time period is $\frac{dT}{T} = \frac{1}{2} \frac{dL}{L}$.Since $\frac{dL}{L} = \alpha \Delta \theta$,we have $\frac{dT}{T} = \frac{1}{2} \alpha \Delta \theta$.Here,$T = 0.5 \ s$,$\alpha = 9 \times 10^{-7} /^{\circ}C$,and $\Delta \theta = 30^{\circ}C - 20^{\circ}C = 10^{\circ}C$.Substituting the values: $dT = T \times \frac{1}{2} \times \alpha \times \Delta \theta$.$dT = 0.5 \times \frac{1}{2} \times (9 \times 10^{-7}) \times 10$.$dT = 0.25 \times 9 \times 10^{-6} = 2.25 \times 10^{-6} \ s$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Mix Examples-Thermometry, Thermal Expansion and Calorimetry

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$A$ clock pendulum having a coefficient of linear expansion $\alpha = 9 \times 10^{-7} /^{\circ}C$ has a period of $0.5 \ s$ at $20^{\circ}C$. If the clock is used in a climate where the temperature is $30^{\circ}C$,how much time does the clock lose in each oscillation? (Assume $g$ is constant)

MHT CET 2019 All MHT CET

A
$2.5 \times 10^{-7} \ s$
B
$5 \times 10^{-7} \ s$
C
$1.125 \times 10^{-6} \ s$
D
$2.25 \times 10^{-6} \ s$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Mix Examples-Thermometry, Thermal Expansion and Calorimetry

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List-$I$	List-$II$
$(A)$ Heat capacity of body	$(I)$ $J kg^{-1}$
$(B)$ Specific heat capacity of body	$(II)$ $J K^{-1}$
$(C)$ Latent heat	$(III)$ $J kg^{-1} K^{-1}$
$(D)$ Thermal conductivity	$(IV)$ $J m^{-1} K^{-1} s^{-1}$

$A$ clock pendulum having a coefficient of linear expansion $\alpha = 9 \times 10^{-7} /^{\circ}C$ has a period of $0.5 \ s$ at $20^{\circ}C$. If the clock is used in a climate where the temperature is $30^{\circ}C$,how much time does the clock lose in each oscillation? (Assume $g$ is constant)

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$A$ hailstone of mass $42 \,g$ falls from a height of $1.8 \,km$. If its entire potential energy is converted into latent heat, what is the mass of the hailstone remaining when it reaches the ground (in $\,g$)? $\left(g=10 \,ms^{-2}, L_{\text{ice}}=3.36 \times 10^5 \,J \,kg^{-1}\right)$

Match List-$I$ with List-$II$.List-$I$List-$II$$(A)$ Heat capacity of body$(I)$ $J kg^{-1}$$(B)$ Specific heat capacity of body$(II)$ $J K^{-1}$$(C)$ Latent heat$(III)$ $J kg^{-1} K^{-1}$$(D)$ Thermal conductivity$(IV)$ $J m^{-1} K^{-1} s^{-1}$Choose the correct answer from the options given below:

The variation of density of water with temperature is represented by the

The heat required to convert $1 \, g$ of ice at $0^{\circ}C$ into steam at $100^{\circ}C$ is (given $L_{f} = 80 \, cal/g$,$c_{w} = 1 \, cal/g^{\circ}C$,$L_{v} = 536 \, cal/g$):

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